Related papers: A nonlinear equation for ionic diffusion in a stro…
The ambipolar diffusion approximation is used to model partially ionised plasma dynamics in a single fluid setting. To correctly apply the commonly used version of ambipolar diffusion, a set of criteria should be satisfied including the…
It is proposed to consider the fast thermalization of gluons in relativistic heavy-ion collisions as a diffusion process in momentum space. Closed-form analytical solutions of a nonlinear boson diffusion equation (NBDE) with constant drift…
Cellular electrophysiology is often modeled using the cable equations. The cable model can only be used when ionic concentration effects and three dimensional geometry effects are negligible. The Poisson model, in which the electrostatic…
The heliosphere is predominantly a partially ionized plasma that consists of electrons, ions and significant neutral atoms. Nonlinear interactions amongst these species take place through direct collision or charge exchange processes. These…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
The Debye-H\"uckel equation is a fundamental physical model in chemical thermodynamics that describes the free energy (chemical potential, activity) of an ion in electrolyte solutions at variable salt concentration, temperature, and…
Spatial interaction effects between charge carriers in ionic systems play a sizable role beyond a classical Maxwellian description. We develop a nonlocal, two-fluid, hydrodynamic theory of charges and study ionic plasmon effects, i. e.…
In this paper we detail the mechanisms that drive substitutional binary diffusion and derive appropriate governing equations. We focus on the one-dimensional case with insulated boundary conditions. Asymptotic expansions are used in order…
We consider the Euler-Poisson system for ions where the electrons are given by a Maxwell-Boltzmann distribution, and we investigate the existence of one-dimensional periodic traveling waves. More precisely, we first establish the existence…
Ion transport in porous media is present in a wealth of technologies, e.g., energy storage devices such as batteries and supercapacitors, and environmental technologies such as electrochemical carbon capture and capacitive deionization.…
Treating water as a linearly responding dielectric continuum on molecular length scales allows very simple estimates of solvation structure and thermodynamics for charged and polar solutes. While this approach can successfully account for…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
Understanding the behavior of biomolecules such as proteins requires understanding the critical influence of the surrounding fluid (solvent) environment--water with mobile salt ions such as sodium. Unfortunately, for many studies, fully…
The ion distribution around charged colloids in solution has been investigated intensely during the last decade. However, few theoretical approaches have included the influence of variation in the dielectric permittivity within the system,…
We consider weakly ionized plasma where frequent elastic scattering of electrons on neutrals change the individual acts and the rate of electron-electron collisions significantly. In this case, the kinetics of electron thermalization is…
This paper considers the probability density and current distributions generated by a point-like, isotropic source of monoenergetic charges embedded into a uniform magnetic field environment. Electron sources of this kind have been realized…
The non-linear Poisson-Boltzmann equation for a circular, uniformly charged platelet, confined together with co- and counter-ions to a cylindrical cell, is solved semi-analytically by transforming it into an integral equation and solving…
Statistically studied are the equilibrium characteristics of a subsystem of mobile charges of one sort, taking into account the subsystem of fixed charges of the opposite sign creating a compensating electric background. The distribution of…
In this letter we analyze the effects of an externally applied electric field on thermal fluctuations for a fluid containing charged species. We show in particular that the fluctuating Poisson-Nernst-Planck equations for charged…
In the present analysis we study the self consistent propagation of nonlinear electromagnetic pulses in a one dimensional relativistic electron-ion plasma, from the perspective of nonlinear dynamics. We show how a series of Hamiltonian…